u-substitution is an extremely useful technique. Harnessing the power of the chain rule, it allows us to define a new variable (common denoted by the letter u) as a function of x, and obtain a new expression which is (hopefully) easier to integrate.
Learn how to use the product rule in order to find the integral of a product of functions (sadly this is more complicated than using the product rule the regular way).
Reverse chain rule is another, faster way to think about u-substitution.
Learn a useful algebraic tool to find the integrals of some rational functions.
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